A partition-of-unity based three-node triangular element with continuous nodal stress using radial-polynomial basis functions

作     者：YANG YongTao ZHENG Hong XU DongDong 

作者机构：State Key Laboratory of Geomechanics and Geotechnical EngineeringInstitute of Rock and Soil MechanicsChinese Academy of Sciences Key Laboratory of Urban Security and Disaster Engineering Ministry of EducationBeijing University of Technology Key Laboratory of Geotechnical Mechanics and Engineering of Ministry of Water ResourcesYangtze River Scientific Research Institute 

出 版 物：《Science China(Technological Sciences)》 (中国科学（技术科学英文版）)

年 卷 期：2017年第60卷第10期

页      面：1518-1536页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：the National Natural Science Foundation of China(Grant Nos.51609240,11572009&51538001) and the National Basic Research Program of China(Grant No.2014CB047100) 

主　　题：partition of unity FE-Meshfree element Trig3-RPlMcns mesh distortion radial-polynomial basis functions 

摘      要：A partition-of-unity （PU） based ＂FE-Meshfree＂ three-node triangular element （Trig3-RPIM） was recently developed for linear elastic problems. This Trig3-RPIM element employs hybrid shape functions that combine the shape functions of three-node triangular element （Trig3） and radial-polynomial basis functions for the purpose of synergizing the merits of both finite element method and meshfree method. Although Trig3-RPIM element is capable of obtaining higher accuracy and convergence rate than the Trig3 element and four-node iso-parametric quadrilateral element without adding extra nodes or degrees of freedom （DOFs）, the nodal stress field through Trig3-RP1M element is not continuous and extra stress smooth operations are still needed in the post processing stage. To further improve the property of Trig3-RPIM element, a new PU-based triangular element with continuous nodal stress, called Trig3-RPIMcns, is developed. Numerical examples including several linear, free vibration and forced vibration test problems, have confirmed the correctness and feasibility of the proposed Trig3-RPIMcns element.